Resulting distributions for Z_th = 8.3, 8.5, and 8.6 as well as no threshold at all (dark blue, blue, light blue, and red, respectively) and κ = 5 and 20 (left and right column, respectively). The higher value of κ corresponds to a sharper cutoff in η_LGRB (see Eq. (16) and Fig. 4), and η₀ is recalculated for each distribution. The red line with no implemented threshold traces the SFR distribution. In the top row we compare the simulated LGRB rates per unit cosmic volume in the source frame of reference (ρ_LGRB; see also panel F in Fig. 6) with the results of Ghirlanda & Salvaterra (2022). In the middle row we show the cumulative distributions of our results for z ≤ 0.5 together with the cumulative distribution of the local LGRB host masses as listed in Appendix A (dark grey CDF, with bins of 0.001). The bottom row shows the cumulative metallicity distributions for z ≤ 2.5 compared to the C17 results of Graham et al. (2023, dark grey CDF, with bins of 0.001). In Appendix B we employ the Kobulnicky & Kewley (2004) MZR to provide a comparison for the KK04 metallicity estimates of Graham et al. (2023). The distributions of the local LGRB host masses and the C17 metallicity estimates were bootstrapped and scattered in order to account for limited sample size and observational uncertainty (as described in Sect. 3), the light grey areas show the 95% confidence intervals. We note that the sampling uncertainty on our model distributions is negligible relative to these confidence intervals.